Use the Laws of Algebra of sets and Logic to prove that: (i)P  Q is logically equivalent to ( P  Q) ? [1 mark] (ii)Find the negations of P  Q ? [3 marks] (iii)Using Truth Table that: P  Q  (P  Q)  (Q  P) ? [2 marks] b) Determine the duality of the Boolean equations (i) (a . 1)  (0  a)  0 [1 mark] (ii) a . (a  b)  a . b

Write the following as a base and exponent

Create a question with this scenario you could ask that could be answered only by graphing or using logarithm. david estimated he had about 20 fish in his pond. a year later, there were about 1.5 times as many fish. the year after that, the number of fish increased by a factor of 1.5 again. the number of fish is modeled by f(x)=20(1.5)^x.

Isabel graphed the following system of equations. 2x – y = 6 y = -3x + 4 she came up with the solution (2,-2). what were the 3 steps she did to get that solution? (make sure they are in the correct order)